The conventional system for connecting handles to cup bodies includes an apparatus for automatically centering a cup body installed on a seat on a movable table and an apparatus for automatically connecting a handle to the cup body centered on the seat. If a cup body is a cylindrical one with no design or pattern on its side wall and with the same diameter at any horizontal cross section thereof, a handle may be correctly connected to the cup body provided that the connection thereof is made at a predetermined height of the side wall of the cup body. Such is also the case with a cup body with different diameters at different horizontal cross sections, but with a true circle at any horizontal cross section thereof. In other words, it may be said that such a cup body has nothing on its side wall which provides a particular direction in which to orientate the cup body. Thus, with the conventional system, handles may be almost automatically connected to a desired number of cup bodies with the same such shapes. However, if, for example, a cup body is a polygonal one, the operation of connecting a handle to such a cup body requires not only observing the predetermined height of connection of the handle, but also orientating the cup body in the right, i.e. as specified or selected, direction for the connection thereof. For example, if a cup body is a polygonal one, usually a handle must be connected as shown in FIG. 8(a), not as shown in FIG. 8(b). Such is also the case with a cup body having a design or pattern on its side wall on which a handle should not be connected. The conventional system, however, has no mechanism for orientating cup bodies in the right direction. Therefore, so far cup bodies have been orientated manually one by one in the right direction.